In order to open up the F battle, you need to be qualified for it first. When you go to the F battle building, where you can enter it, there are markings and some list of qualifying tournament to finish before you are elligible to enter.

In order to open the qualifying tournament, you must do some tournament first. To make is simple, tournament that requires cosplay parts or specific shinki is not important. Only the tag, normal and weapon limit tournament that are required for.

For weapon limit restrictions, here is the copy from page 40 to help you out.

Hey peoples...I know its been a while but I was a tad preoccupied since I last posted

Anywho...

If I'm here today its to ask possibly dumb questions and drink cappucino lattes...and I'm all out of the latter

So my first question is:

I cleared F1....YAY....That pink haired Arnval was a total pushover considering She could only hit me once and it didn't even do anything remarkable damage-wise...To my strarf wich I just LOVE using...

Now I saw a scene where I SUPPOSE a bomb went off SOMEWHERE and I can't do anything anymore...The hell's going on ?

And my second question is

Now lets assume I have money to spend and I am willing to get myself some DLCs

Considering I live in france and that I KNOW I can buy 20 euros codes for the PSN store, what would be the steps to follow...

It's okay. Follow these steps, this should get you out of that locked event where you can't do anything.

Go to the Shop
Go to the F battle building
Enter the F battle building one more time
Go back to your house and watch that BSB news again
Go to the F battle building again where you get a Pendant with a photo inside (white out though so you can’t see). This is story item.
Go back to the house with that dreaded BSB news again

After going out from you bunk (er….you house) you’ll see an event of two people (conveniently named Man A and Man B )talking something quite rude and offensive about shinkis. Your shinki reaction is just asking to go home and ignore them (Though Arnval and Altlene seems completely uncertain and troubled…..seems these two are the most clingy to the master). Oh well, at least now all shinki battle at Game Center, Tournament and club Valhalla is now open again with quite some number of new battle (with one of them is a hilarious Altlene mimicking a super hero entrance style (complete with Visual and Sound Effect!) where most of your shinki either says it is cool or surprising….but your Altlene will say it is very embarrassing and Baby Razz actually angry saying that she is stealing the show from her). Like usual go to the game center 1st and beat the crap out of all new opponent.

Should get you out of trouble and can play again.

And as far as DLC, I kinda forgot (been a long time since I got the DLC). But IRC, you need JPN PSN codes to buy the DLC.

Well, no fear, you can get DLC. For that, you need to open a japanese account (there are tutorials around the net to show you how to do that).
For the DLC themselves, I used Media Go on my PC to access the japanese shop.

Once on the shop : you have this menu

You need to click the 6th one, just before the one ending with PV.
Then, you need to scroll down until you find this :

You then get the choice between different hiragana to find your game, so click on this one :